Import Question JSON

Current Question (ID: 20908)

Question:

$\text{Consider the following statements:}$ $\text{Statement I:}$ \text{The number of emitted photoelectrons increases with increase in the frequency of incident light.}$ $\text{Statement II:}$ \text{The kinetic energy of emitted photoelectrons increases with increase in the frequency of incident light.}$

Options:

1. $\text{Statement I is true but Statement II is false.}$
2. $\text{Statement I is false but Statement II is true.}$
3. $\text{Both Statement I and Statement II are true.}$
4. $\text{Both Statement I and Statement II are false.}$

Solution:

$\text{Hint: The number of emitted photoelectrons does not depend on the frequency of the incident light.}$ $\text{Explanation:}$ $\text{The statement that "the number of emitted photoelectrons increases with an increase in the frequency of incident light" is not entirely accurate.}$ $\text{Each material has a threshold frequency } (\nu_0), \text{ below which no photoelectrons are emitted, regardless of the intensity of the light.}$ $\text{This frequency corresponds to the minimum energy required to liberate an electron from the material's surface.}$ $\text{As you increase the frequency of incident light (beyond its threshold), you provide more energy to each photon, which results in higher kinetic energy for emitted photoelectrons.}$ $\text{This relationship is fundamental to understanding how light interacts with matter and forms a cornerstone of quantum mechanics and modern physics.}$ $\text{The number of emitted photoelectrons is independent of the frequency of incident light but the kinetic energy of emitted photoelectrons increases with an increase in the frequency of incident light.}$ $\text{Hence, option 2 is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}